What is the solution to –2|2.2x – 3.3| = –6.6?

Question

campbell_st · Answer

so what do you think the 1st step should be?

vickx49 · Answer

First, I distributed -2

vickx49 · Answer

I tried this and got an answer of x = 3, but I want to make sure it's correct. Thanks for your help

campbell_st · Answer

not quite... 

try dividing both sides of the equation by -2

it's easier then trying to distribute -2 in an absolute value equation...

campbell_st · Answer

so what would you get..?

vickx49 · Answer

3.3

vickx49 · Answer

|2.2x – 3.3| = 3.3 to be exact

vickx49 · Answer

Oh, yup the answer is x = 3 after you add and divide again. Thanks!

campbell_st · Answer

great so you have the absolute value equation 

$$\left| 2.2x -3.3 \right| = 3.3$$

so when you deal with absolute value equations of this type there could be 2 solutions

so you need to solve

2.2x - 3.3 = 3.3         as well as     2.2x - 3.3 = - 3.3

now solve for x... and check by substituting the solutions into the original equations to see if they make sense.

campbell_st · Answer

well I think you need to be careful... because if this is an absolute value equation there are 2 solutions.

vickx49 · Answer

Oh, I completely forgot to figure out the negative and positive. lol

vickx49 · Answer

So I believe the two solutions are x = 0 and 3. Correct?

vickx49 · Answer

*-3

marcelv · Answer

Plugging on the original is not enough, absolute value definition makes it positive if the inside is positive, like |4| = 4, but if we have a negative number then it is like we are making the inside negative |-3| = -3 $$|2.2x-3.3| < 3.3$$ At that step we have to check if the inside is poitive or negative, so we have 2 cases to check. $$ \begin{cases} 
      2.2x-3.3 = 3.3 & \text{ if } 2.2x-3.3\geq 0 \
      -(2.2x-3.3) = 3.3 & \text{ if }  2.2x-3.3 < 0 
   \end{cases}
$$ The idea is that once you solve for each you have to plug and verify on the inequalities, and not on the original equation

So for the positive case we got x =3 and if we plug it on the inequality we have 3.3 > = 0 so it is true, x = 3 is a good answer, and for hte other equation we get x = 0, then -3.3 < 0 is true as well so both are good answers.

campbell_st · Answer

that's correct, x = 0 and x = 3